Question 115090
If the polynomial is a perfect square, then there is an a such that
{{{x^2-24x+48=(x+a)^2}}}
You can expand the right hand side and match up terms.
{{{x^2-24x+48=x^2+2ax+a^2}}}
You have to satisfy two terms for the equation to be a perfect square
1.{{{-24x=2ax}}}
2.{{{48=a^2}}}
From 1,
1.{{{-24x=2ax}}}
{{{-24=2a}}}
{{{highlight(a=12)}}}
From 2,
2.{{{48=a^2}}}
{{{a=sqrt(48)}}}
{{{highlight(a=6.93)}}}
Since you can't satisfy both requirements 1 and 2, the polynomial is not a perfect square.